On plane algebroid curves

Details On plane algebroid curves On plane algebroid curves

2003-02-19

arxiv.org/abs/math/0302224v1

Lecture Notes Pure Appl. Math. 231 (2003), 37-50

Mathematics

Commutative Algebra

14 pages

Scientific paper

Two plane analytic branches are topologically equivalent if and only if they have the same multiplicity sequence. We show that having same semigroup is equivalent to having same multiplicity sequence, we calculate the semigroup from a parametrization, and we characterize semigroups for plane branches. These results are known, but the proofs are new. Furthermore we characterize multiplicity sequences of plane branches, and we prove that the associated graded ring, with respect to the values, of a plane branch is a complete intersection.

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